The suggestion that we occupy a privileged position near the centre of a
large, nonlinear, and nearly spherical void has recently attracted much
attention as an alternative to dark energy. Putting aside the philosophical
problems with this scenario, we perform the most complete and up-to-date
comparison with cosmological data. We use supernovae and the full cosmic
microwave background spectrum as the basis of our analysis. We also include
constraints from radial baryonic acoustic oscillations, the local Hubble rate,
age, big bang nucleosynthesis, the Compton y-distortion, and for the first time
include the local amplitude of matter fluctuations, \sigma_8. These all paint a
consistent picture in which voids are in severe tension with the data. In
particular, void models predict a very low local Hubble rate, suffer from an
"old age problem", and predict much less local structure than is observed.

The authors have done a thorough analysis of different observational constraints (e.g. CMB, SNe, BAO, \sigma_8, ...) and seem to rule out inhomogeneous models with a large void. Any opinions on this work?

This indeed looks very thorough, but I was confused by the different claims of this other recent paper: 1007.3065 that says they can fit a similar collection of data (albeit neglecting sigma_8) by allowing nonzero spatial curvature combined with a varying void profile to match larger H0 values. It looks to me like Moss et al. include such scenarios in their analysis, including quite general void profiles that fail to alleviate the low H0 prediction.

Can anyone explain the apparently discrepant claims between these two papers?

Embedding these voids in a non-flat background helps fit the CMB peaks as the shift parameter is mostly sensitive to spatial curvature at high z, rather than low (see 0902.1313). This also helps the problem with low H0 a bit, but not by enough.

It looks like Biswas et al. (1007.3065) also have a low H0 problem in a similar way to Moss et al. They seems to find that very very wide voids help alleviate this a bit, but even in this case it looks like H0 is a little low (h=0.62 to 2 sigma, is this too low?).

Possible ways of getting more acceptable H0 are to include inhomogeneous radiation fields, as in Clarkson and Regis (1007.3443), or allowing a non-simultaneous big bang, as in 0902.1313.

About the confusion: in both papers the finding is that voids embedded in an EdS metric are ruled out. So the technical results from both papers are really in agreement. It is just that since in 1007.3065 we also consider global curvature (as Timothy explains), and find good overall fits (that is, simultaneous CMB+BAO+HST+SN, where H0 being only one datapoint can easily be off by 2 \sigma), we draw a completely different overall conclusion. But yes, h~60 may not be good enough, although this depends on your choice of datapoints as well. If you take for example H_0=62 from astro-ph/0603647, you'll see that the void can gives almost exactly as good a fit as LCDM to CMB+BAO+HST+SN.. Anyway, to remain conservative, we provide fits to other H_0-values as well.

One significant difference is for the BAO though. In 1007.3725 the authors fit the radial BAO only, which seems to favour LCDM over voids. In 1007.3065 we fit the 'complete' BAO (so radial times angular scales), which seems to favour voids over LCDM. It is not clear to me which of the two approaches is more fair. Does anyone have an idea?

Having said that, 1007.3065, 1007.3443 and 1007.3725 came out practically simultaneously, agree in the principle results, but apart from that addressed different issues. So one should really read them all.... (that should help taking away the confusion.)

About the apparent discrepancy between our paper and Biswas et al, 1007.3065, I'd note that for their higher local Hubble rate cases, Biswas et al find very large local curvature parameter, [tex]\Omega_{k,in}[/tex], as their Table XIII shows. According to that table, their higher local [tex]H_0[/tex] profiles require what we would consider unrealistically high local [tex]\Omega_{k,in}[/tex], eg. [tex]\Omega_{k,in} = 0.936[/tex] or [tex]0.984[/tex]. In our study we imposed what we considered a conservative prior of [tex]\Omega_k < 0.9[/tex] at the void centre today. We suspect this is the source of the discrepancy. Even so, it seems their highest [tex]H_0[/tex] value (57 km/s/Mpc) is still low compared with most local estimates.

About the BAO, we argued in our paper that the angular scale should be a weaker discriminator from LCDM because it depends on the angular diameter distance, which is basically tuned in void models to fit the LCDM angular distance. The radial scale is a very strong discriminator, and the only question is about the statistical significance of the radial BAO data.

Having said this, I agree with Wessel that it looks as though our two papers are largely in agreement.

Yes, it is true that we allow for any value for \Omega_{k,in} (the curvature at the center of the void) in 1007.3065. But as H_{0,in} (the observed local Hubble rate) mostly depends on [tex]\Omega_{k,in}[/tex], the 5% difference in local curvature (\Omega_{k,in}=0.935 in 1007.3065 in stead of 0.9 in 1007.3725) does not explain the 25% difference in H_{0,in} (57 vs 45). I think the effect is two-fold, one is the higher local curvature, but the other (and that is the main finding in 1007.3065) is the global curvature which has a significant effect on the distance to last scattering, and hence allows for playing with the expansion rate.

For example, the model in 1007.3065 with the highest [tex]H_{0,in}[/tex] also has a CMB temperature today of 4.54 K (where the observed temperature is still 2.726K, as it is redshifted due to the void). A universe so young yet with the correct distance to last scattering, is only possible with a global curvature term.

By playing more with curvature profiles, I think it is possible to get an even higher H0. The more solid observation that can rule out even these very empty voids that nevertheless could fit HST, seems to me to be the compton-y scattering and [tex]\sigma_8[/tex] that you have addressed in 1007.3725 for the first time.

It's much more than a 5% difference. 0.9 was our cutoff. Our best fit [tex]\Omega_{k,in}[/tex] is roughly 0.8, as our Fig 5 shows. I agree that the details of the void profile and whether there's spatial curvature outside the void or not will have an effect on how high we can get [tex]H_0[/tex], but it will be a subdominant effect to the local curvature.

Maybe it is important to point out that we are fitting different observations in the papers. In 1007.3725 you always fit the local [tex]\sigma_8[/tex], which weighs in on the allowed values for [tex]\Omega_{matter,in}[/tex], as you pointed out (private). In the fits where we included the matter power spectrum in 1007.3065, we also found much lower [tex]\Omega_{k,in}[/tex] and hence low [tex]H_{0,in}[/tex]. On the other hand, the profiles that led to a high [tex]H_{0,in}[/tex], change so significantly around the redshifts relevant for the large scale structure, that we didn't want to fit them with an effective FLRW. So I think the source of different [tex]\Omega_{k,in}[/tex] is not so much the prior, as it is the data that one fits.

About the global curvature being subdominant: yes, you're absolutely right, the main ingredient is [tex]\Omega_{k,in}[/tex]. But, the two values you quoted from our paper for [tex]\Omega_{k,in}[/tex], 0.98 and 0.93, are for models that do predict the same [tex]H_{0,in}[/tex]. The difference is the shape of profile and the global curvature..

It would be good to be able to calculate some LSS for the rapidly varying profiles too... Work to do!

Just one more clarification: our allowed values of [tex]\Omega_{k,in}[/tex] (our Fig 5) are determined solely by the CMB + SN data (mostly the SNe, actually). But I agree that pushing the profiles towards larger [tex]\sigma_8[/tex] would mean pushing them towards smaller [tex]\Omega_{k,in}[/tex], since models with smaller [tex]\Omega_k[/tex] will experience less suppression of perturbation growth.